A COMPARISON OF SIMPLIFIED ENGINEERING AND FEM METHODS FOR ON-

Muk Chen Ong

University of Stavanger NO-4036, Stavanger, Norway

Keywords: On-bottom stability, simplified method,

ABSTRACT hydrodynamic load, finite element analysis. This paper presents a comparison between simplifiedengineering and FEM (Finite Element Method) methods for on- INTRODUCTIONbottom stability analysis of a subsea pipeline. The simplifiedengineering method is first used to assess the absolute on- A standard engineering task when designing subsea pipelines isbottom stability of empty and filled pipelines under different to ensure that the pipeline is stable on the seabed under thescenarios. The calculations of the hydrodynamic loads for action of hydrodynamic loads induced by waves and steadythree scenarios, i.e. steady current alone, regular waves alone currents. If it is too light, it will slide sideways under the actionand combined regular waves and current, are implemented in of hydrodynamic forces. If it is too heavy, it will be difficultMATLAB code. The drag and lift coefficients are determined and expensive to construct. This movement of the pipeline willbased on Keulegan-Carpenter number, Reynolds number and cause bending stresses on the pipe, which may then cause thesurface roughness of the pipelines. Only the friction force is pipe to fatigue and fail. Simultaneously, it may cause damage toconsidered in the simplified methods. In order to achieve the the coatings, for example, cracking of concrete. Conventionallyabsolute stability, the vertical (lift force/submerged weight<1) a subsea pipeline has been considered stable if it has gotand horizontal (in-line force/friction force<1) criteria need to be sufficient submerged weight so the lateral soil resistance isfulfilled at same time. Time-domain dynamic on-bottom sufficiently high to restrain the pipeline from deflectingstability analysis is performed by PONDUS for the same cases. sideways.The results of water particle velocity, hydrodynamic force, liftforce and soil resistance force are compared between the On-bottom stability calculations are performed to establishsimplified engineering and advanced FEM methods. Their requirements for pipeline submerged mass. The requiredresults are in good agreement for the cases, which fulfills the pipeline submerged mass will have a direct impact on theabsolute on-bottom stability criterion. For the cases which the required pipe-lay tensions, installation stresses and the pipepipelines will move under the combined wave and current configuration on the sea bottom. Subsea pipeline stability isloadings, the soil resistance force predicted by the simplified governed by the fundamental balance of forces between loadsengineering method is different from that of the FEM method. and resistances. From the installation viewpoint, especiallyThe study shows that for engineering purpose the simplified where spans are not a concern, the priority is to minimize theengineering method could be used to check the absolute on- required pipeline submerged weight [3].bottom stability of the pipeline, whereas the more advancedFEM method needs be performed when the pipeline is allowed The general on-bottom stability analysis involves the followingto move within a limited distance. procedures [1]: Step 1: Data gathering for the 1-year and 100-year environmental conditions, which includes:

SIMPLIFIED METHODThe forces acting on the pipe are shown in Figure 1. U is theflow velocity acting on the pipeline, FL is the lifting force,Finline is the in-line force, F is the friction between the The environment data applied in the analysis is presented inpipeline and the seabed, and Fg is the submerged weight with Table 3.buoyancy taken into account. Table 3 Environment data Environment data Return period 1 year 10 year 100 year Wave height H (m) 10.3 12.6 14.8 Wave period T (s) 13.2 14.7 15.9 Current velocity (m/s) 0.36 0.51 0.66 (1m above seabed) Water depth (m) 104

As the current velocity ( ) is given at 1m above the

seabed, the mean perpendicular current velocity over a pipeFigure 1 Force acting on the pipe diameter is determined according to [2].

In order to verify stability two equations have to be fulfilled in 1 + 0 + 1 1 0order to insure that the pipeline will not move. = ( ) () + 1Horizontal: 1.0 = 0 where zr is the reference measurement height over sea bed.Vertical: 1.0 Z0 is Bottom roughness parameter.Where is the friction coefficient. D is the outer diameter of the pipe.

The pipe and soil properties used in analysis are presented in The on-bottom stability of pipeline is performed usingTable 1 and the material properties are listed in Table 2. simplified method for two conditions as following: Empty pipe - temporary condition Filled pipe - operation condition

The roughness of the pipeline k/D is 0.001 and only the friction force is considered in the simplified method. Another assumption regarding environment condition is that there is only regular wave considered in the present study, and the stability of the pipeline (empty and filled) under hydrodynamic loading for the following three different scenarios is analyzed:

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Steady current alone o Empty (temporary) condition Waves alone 1-year return condition for waves and 10-year return Combined wave and current. condition for currentThe calculations of the hydrodynamic loads for three scenarios 10-year return condition for waves and 1-year returnare implemented in MATLAB code. condition for current o Filled (permanent/operation) condition: 10-year return condition for waves and 100-year returnSteady current alone condition for current 100-year return condition for waves and 10-year returnFor steady current alone only Reynolds number is calculated to condition for currentdetermine the drag and lift coefficient and this number tellswhich flow regime the pipe is in, describing the water flow The flow velocity U is the sum of current velocity Uc and wavearound a cylindrical shaped object. Keulegan-Carpenter number velocity Uw:(KC number) is zero. = + The in-line and lift force: = 1 = || + - Kinematic viscosity of salt water at 20 degrees 2 1 2 = The drag and lift force is calculated by: 2 1 The Re is calculated by maximum flow velocity and KC is = 2 calculated by maximum wave induced velocity. 2 1 = = 2 2 =Wave alone is maximum flow velocity.A cylinder subjects to oscillatory flow may experience twokinds of forces: the in-line force and the lift force. Analysis resultsThe in-line force per unit length of the cylinder is calculated bythe Morison equation: 1 Empty pipe = | | + 2 The force consists of two parts: drag force and hydrodynamic The calculated results from MATLAB code for empty pipe aremass force. shown in Table 4 and Table 5. The horizontal stability is not is wave induced velocity. fulfilled for case 4 and after the thickness of concrete coating is is the inertia coefficient. increased from 55 mm to 75 mm in case 5 the absolute A is the cross-sectional area of the cylinder. stability of the pipe is fulfilled.

The lift force is calculated by: The velocity and force components acting on the empty pipe 1 under 10-y wave alone and combined 1-y current and 10-y = 2 wave are shown in Figure 2 and Figure 3. The drag force is 2 proportional to the flow velocity square and changes directionThe drag, Inertia and lift coefficient is dependent on KC, Re with flow, and the hydrodynamic mass force is proportional toand surface roughness [9]. the flow acceleration and changes direction with acceleration. The lift force is proportional to flow velocity square and is = always upwards.

= The in-line force is a combination of the drag and inertia forces. is maximum wave induced water particle velocity. Due to the 90 degree of phase difference between water particle velocity and acceleration in regular wave the occurrence ofCombined wave and current maximum force of drag and inertial force has 90 degree phase different. The hydrodynamic force consists obviously of moreTwo load combinations for both empty and filled conditions are than one harmonic component. The amplitude ratio betweenanalyzed according to DNV RP-109. drag and inertia forces varies significantly depending on the

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wave frequency and the current to wave-induced velocity ratio;and the inertia becomes more important for small waves and aweak current. For the cases with combined current and waveloading the drag and lift forces are shifted upwards due tocurrent.

3 3 1.1 4 398.8 1151 491 1970 0.58 0.81

4 3 1.5 3.4 714.8 1408 336.7 1970 0.72 2.12

The calculated results from MATLAB code for filled pipe are shown in Table 6 and Table 7. The horizontal stability is not fulfilled for case 9 and after the thickness of concrete coating is increased from 55 mm to 75 mm in case 10 the absolute stability of the pipe is fulfilled.

7 3.3 1.4 2.5 718.2 1016 1781.3 3984.8 0.25 0.43

10 3.3 1.4 2.5 1327 2247 1444 4882.8 0.48 0.92

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The velocity and force components acting on the empty pipe FINITE ELEMENT METHODunder 10-y wave alone and combined 1-y current and 10-ywave are shown in Figure 4 and Figure 5. The force PONDUS developed by MARINTEK is software focusingcomponents show same characteristic as those for empty pipe. specifically on the dynamic lateral response of offshore pipeline subject to a combined action of wave and current on a horizontal seabed.

The Main features of PONDUS software is listed below:

Calculates the wave kinematics from 3-D irregular waves for medium and deep water Calculates the hydrodynamic force by load models Morrison Database force model [6] Combination of Morrison and Database force model Uses 2-D beam elements with small deflection theory in the finite element formulation Calculates the soil resistance forces by soil model Sand soil [8] Clay soil [7] Computes the dynamic response of pipeline subjected to wave and current in time domain for pipeline on horizontal seabed

The cases with combined current and wave loading are most relevant in real sea and case 4 and 5 for empty pipe and case 9 and 10 for filled pipe are analyzed by PONDUS. The sameFigure 4 Velocity and forces acting on the empty pipe with drag, inertial and lift coefficient are applied in the PONDUS100-y wave (case 7). analysis.

Assume the pipe length is 250 meters. The pipe is divided to 50

elements in the model, and the boundary condition is defined as fellow: Fixed in translation and rotation at the left end. Fixed in rotation at the right end. The response of pipe are taken from the right end (node 51), and the simulation time is set as 2400 seconds.

Figure 6 Illustration of PONDUS model

Analysis results

Empty pipe

Figure 5 Velocity and forces acting on the empty pipe with For case 4 the maximum pipe displacement occurs at node 5110-y current and 100-y wave (case 9). and it reaches about 4.5 m after 1000s. The requirement for absolute stability is obvious not fulfilled and the lateral

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displacement may meet the requirement of the maximumallowed displacement 10D.

Figure 10 Lift force (case 4)

Figure 7 Displacement at node 51 (case 4)

The results of water velocity, hydrodynamic force, lift force and

soil friction force during first 100 seconds are shown in Figure8 to Figure 11. The maximum value of water velocity,hydrodynamic force, lift force and soil friction force arepresented in Table 8.

The comparison of the soil force is more complicated, for cases

5 and 10 which pipe is absolutely stable the friction forces havegood agreement between simplified and FEM method. For thecases 4 and 9 the pipe displaces due to hydrodynamic loading,and it shows that the soil friction forces are different forsimplified and FEM method. The deviation is likely due to thatthe minimum friction force is used in the simplified engineeringcalculation to obtain the safety factor, while friction forceactually varies by time in PONDUS simulation when the pipe isin an unstable state.

CONCLUSIONS

The study shows that for engineering purpose the simplified

engineering method could be used to check the absolute on-bottom stability of the pipeline, whereas the more advancedFEM method needs be performed when the pipeline is allowedto move within a limited distance. PONDUS simulationprovides the transient variance of the friction force on the pipein its unstable state.